Global well‐posedness for compressible Navier‐Stokes equations with highly oscillating initial velocity

By Qionglei Chen, Changxing Miao, Zhifei Zhang. 2009

255 citations recorded by the source corpus.

In this paper, we prove global well‐posedness for compressible Navier‐Stokes equations in the critical functional framework with the initial data close to a stable equilibrium. This result allows us to construct global solutions for the highly oscillating initial velocity. The proof relies on a new estimate for the hyperbolic/parabolic system with convection terms. © 2010 Wiley Periodicals, Inc.

Subfields: Applied Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/5d8d629658db59e9a3924871b4e784158968462e

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In Applied Mathematics

1. Changxing Miao
2. Boris Haspot
3. Qionglei Chen
4. Zhifei Zhang
5. Jiahong Wu
6. Zhen Lei
7. Sadek Gala
8. Taoufik Hmidi

In Control and Systems Engineering

1. Changxing Miao
2. Boris Haspot
3. Zhifei Zhang
4. Qionglei Chen
5. Jiahong Wu
6. Sadek Gala
7. Zhen Lei
8. Taoufik Hmidi

Citations in the corpus

• ON THE ILL-POSEDNESS OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS (2011, background): “Very recently, important progress has been made by Chen-Miao-Zhang [6] and Charve-Danchin [4] where they construct the global solution for the highly oscillating initial velocity for the baratropic Navier-Stokes equations by proving the global well-posedness of the system (1.”
• Existence of Global Strong Solutions in Critical Spaces for Barotropic Viscous Fluids (2010, background): “So as in [11] and [7], the system has to be handled differently in low and high frequencies.”